Structured Gamma

The Gamma language is based on the chemical reaction metaphor which has a number of benefits with respect to parallelism and program derivation. But the original definition of Gamma does not provide any facility for data structuring or for specifying particular control strategies. We address this issue by introducing a notion of structured multiset which is a set of addresses satisfying specific relations. The relations can be seen as a form of neighborhood between the molecules of the solution; they can be used in the reaction condition of a program or transformed by the action. A type is defined by a context-free graph grammar and a structured multiset belongs to a type T if its underlying set of addresses satisfies the invariant expressed by the grammar defining T . We define a type checking algorithm that allows us to prove mechanically that a program maintains its data structure invariant. We illustrate the significance of the approach for program refinement and we describe its application to coordination.